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Exercise

$\frac{d}{dx}\left(9x^{-x}\right)$

Step-by-step Solution

1

The derivative of a function multiplied by a constant is equal to the constant times the derivative of the function

$9\frac{d}{dx}\left(x^{-x}\right)$
2

The derivative $\frac{d}{dx}\left(x^{-x}\right)$ results in $\left(-\ln\left(x\right)-1\right)x^{-x}$

$9\left(-\ln\left(x\right)-1\right)x^{-x}$

Final answer to the exercise

$9\left(-\ln\left(x\right)-1\right)x^{-x}$

Try other ways to solve this exercise

  • Choose an option
  • Find the derivative using the definition
  • Find the derivative using the product rule
  • Find the derivative using the quotient rule
  • Find the derivative using logarithmic differentiation
  • Find the derivative
  • Integrate by partial fractions
  • Product of Binomials with Common Term
  • FOIL Method
  • Integrate by substitution
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